Question

Write the following in roster form. 

(i) {x ∈ N : x² < 121 and x is a prime}. 

(ii) the set of all positive roots of the equation (x – 1)(x + 1)(x² – 1) = 0. 

(iii) {x ∈ N : 4x + 9 < 52}. 

(iv) {x : (x - 4)/(x + 2) = 3, x ∈ R – {-2}}

Answer 1

(i) A = {2, 3, 5, 7} 

(ii) B = {1} 

(iii) 4x + 9 < 52 

4x + 9 – 9 < 52 – 9

4x < 43 

x < (43/4) (i.e.) x < 10.754 

But x ∈ N 

∴ A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

(iv) {x : (x - 4)/(x + 2) = 3, x ∈ R – {-2}}

(x - 4)/(x + 2) = 3

(x - 4)(x + 2)/(x + 2) = 3(x + 2) {∴ ≠ x - 2}

(i.e.) x – 4 = 3(x + 2) 

x – 4 = 3x + 6 

– 4 – 6 = 3x – x 

2x = -10 ⇒ x = -5 

A = {-5}